Mixed conductor, electrochemical device including the same, and method of preparing the mixed conductor

ABSTRACT

A mixed conductor represented by Formula  1:    
       A 1±X M 2±y O 4−δ   Formula  1  
 
     wherein, in Formula  1,  A is a monovalent cation, and M is at least one of a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, a pentavalent cation, or a hexavalent cation,  0 ≤x≤ 1, 0 ≤y≤ 2,  and  0≤δ≤1,  with the proviso that when M includes vanadium,  0&lt;δ≤1,  and wherein the mixed conductor has an inverse spinel crystal structure.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and the benefit of U.S. ProvisionalApplication No. 62/749,845, filed on Oct. 24, 2018, in the U.S. Patentand Trademark Office, and Korean Patent Application No. 10-2018-0167759,filed on Dec. 21, 2018, in the Korean Intellectual Property Office, andall the benefits accruing therefrom under 35 U.S.C. § 119, the contentsof which are incorporated herein in their entirety by reference.

BACKGROUND 1. Field

The present disclosure relates to a mixed conductor, an electrochemicaldevice including the same, and a method of preparing the mixedconductor.

2. Description of the Related Art

In electrochemical devices such as a battery, an electrochemicalreaction occurs in which ions and electrons move along separatemigration paths between electrodes to be combined at the electrodes.

In the electrodes, an ionic conductor for conducting ions and anelectronic conductor for conducting electrons are mixed and arranged.

Nonetheless, there is a need for an improved battery material, e.g., amaterial which is chemically stable to byproducts of electrochemicalreactions and conducts both ions and electrons.

SUMMARY

Provided is a mixed conductor which is chemically stable and may conductboth ions and electrons.

Provided is an electrochemical device including the mixed conductor.

Provided is a method of preparing the mixed conductor.

Additional aspects will be set forth in part in the description whichfollows and, in part, will be apparent from the description, or may belearned by practice of the presented embodiment.

According to an aspect of an embodiment, there is provided a mixedconductor represented by Formula 1

A_(1±x)M_(2±y)O_(4−δ)  Formula 1

wherein, in Formula 1, A is a monovalent cation, M is at least one of amonovalent cation, a divalent cation, a trivalent cation, a tetravalentcation, a pentavalent cation, or a hexavalent cation, 0≤x≤1, 0≤y≤2,0≤δ≤1,with the proviso that when M includes vanadium, 0<δ≤1.

Also disclosed is an electrode including: a current collector; and themixed conductor on the current collector.

According to an aspect, an electrochemical device includes a cathode; ananode; and an electrolyte between the cathode and the anode, wherein atleast one of the cathode, the anode, and the electrolyte include themixed conductor.

According to an aspect of another embodiment, a method of preparing themixed conductor includes: mixing an A-element containing precursor andan M-element containing precursor to prepare a mixture; and thermallytreating the mixture in a solid phase to prepare the mixed conductor.

BRIEF DESCRIPTION OF THE DRAWINGS

These and/or other aspects will become apparent and more readilyappreciated from the following description of the embodiment, taken inconjunction with the accompanying drawings in which:

FIG. 1 is a graph of intensity (arbitrary units, a.u.) versusdiffraction angle (degrees two-theta (2θ)) illustrating X-raydiffraction (“XRD”) spectra of the mixed conductors prepared in Examples1 to 3, in which the spectra of Examples 1 and 2 are offset for clarity;

FIG. 2 is a graph of Density of States versus Energy (electron volts,eV) illustrating the results of density of states (“DOS”) analysis of aLi₄Ti₅O₁₂ conductor of Comparative Example 1;

FIG. 3 is a schematic view illustrating a spinel crystal structure ofLi₄Ti₅O₁₂;

FIG. 4 is a schematic view of a portion of an inverse spinel crystalstructure of LiFe₂O₄, which is a mixed conductor according to Example 1;and

FIG. 5 is a schematic view illustrating an embodiment of a structure ofa lithium-air battery.

DETAILED DESCRIPTION

The present inventive concept will now be described more fully withreference to the accompanying drawings, in which example an embodimentis shown. The present inventive concept may, however, be embodied inmany different forms, should not be construed as being limited to theembodiment set forth herein, and should be construed as including allmodifications, equivalents, and alternatives within the scope of thepresent inventive concept; rather, this embodiment is provided so thatthis inventive concept will be thorough and complete, and will fullyconvey the effects and features of the present inventive concept andways to implement the present inventive concept to those skilled in theart.

The terminology used herein is for the purpose of describing aparticular embodiment only and is not intended to be limiting. As usedherein, “a”, “an,” “the,” and “at least one” do not denote a limitationof quantity, and are intended to include both the singular and plural,unless the context clearly indicates otherwise. For example, “anelement” has the same meaning as “at least one element,” unless thecontext clearly indicates otherwise. “At least one” is not to beconstrued as limiting “a” or “an.” “Or” means “and/or.” “At least one”is not to be construed as limiting “a” or “an.” “Or” means “and/or.” Asused herein, the term “and/or” includes any and all combinations of oneor more of the associated listed items. It will be further understoodthat the terms “comprises” and/or “comprising,” when used in thisspecification, specify the presence of stated features, integers, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, integers, steps,operations, elements, components, and/or groups thereof. The sign “/”used herein may be construed as meaning “and” or “or,” unless thecontext clearly indicates otherwise.

In the drawings, the size or thickness of each layer, region, or elementare arbitrarily exaggerated or reduced for better understanding or easeof description, and thus the present inventive concept is not limitedthereto. Throughout the written description and drawings, like referencenumbers and labels will be used to denote like or similar elements. Itwill also be understood that when an element such as a layer, a film, aregion or a component is referred to as being “on” another layer orelement, it can be “directly on” the other layer or element, orintervening layers, regions, or components may also be present. Althoughthe terms “first”, “second”, etc., may be used herein to describevarious elements, components, regions, and/or layers, these elements,components, regions, and/or layers should not be limited by these terms.These terms are used only to distinguish one component from another, notfor purposes of limitation.

Spatially relative terms, such as “beneath,” “below,” “lower,” “above,”“upper” and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, the exemplary term “below” can encompass both anorientation of above and below. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein interpreted accordingly.

“About” or “approximately” as used herein is inclusive of the statedvalue and means within an acceptable range of deviation for theparticular value as determined by one of ordinary skill in the art,considering the measurement in question and the error associated withmeasurement of the particular quantity (i.e., the limitations of themeasurement system). For example, “about” can mean within one or morestandard deviations, or within ±30%, 20%, 10% or 5% of the stated value.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this disclosure belongs. It willbe further understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art and thepresent disclosure, and will not be interpreted in an idealized oroverly formal sense unless expressly so defined herein.

Exemplary embodiments are described herein with reference to crosssection illustrations that are schematic illustrations of idealizedembodiments. As such, variations from the shapes of the illustrations asa result, for example, of manufacturing techniques and/or tolerances,are to be expected. Thus, embodiments described herein should not beconstrued as limited to the particular shapes of regions as illustratedherein but are to include deviations in shapes that result, for example,from manufacturing. For example, a region illustrated or described asflat may, typically, have rough and/or nonlinear features. Moreover,sharp angles that are illustrated may be rounded. Thus, the regionsillustrated in the figures are schematic in nature and their shapes arenot intended to illustrate the precise shape of a region and are notintended to limit the scope of the present claims.

As used herein, the term “mixed conductor” refers to a conductorconcurrently having suitable ionic conductivity and suitable electronicconductivity. The mixed conductor exhibits improved ionic conductivityand electronic conductivity at the same time, as compared withLi₄Ti₅O₁₂.

“Spinel structure” as would be understood by an artisan in the solidstate sciences and as is used herein means that the compound isisostructural with spinel, i.e., MgAl₂O₄ In a spinel structure, a cationcorresponding to Al occupies an octahedral site and the cationcorresponding to Mg occupies a tetrahedral site.

“Inverse spinel structure” as would be understood by an artisan in thesolid state sciences and as is used herein means that the compound isisostructural with Fe₃O₄, in which the cations corresponding to Fe²⁺ andhalf of the cations corresponding to Fe³⁺ occupy a octahedral site, andthe other half of the cations corresponding to Fe³⁺ occupy a tetrahedralsite.

Hereinafter, an embodiment of a mixed conductor, an electrochemicaldevice including the mixed conductor, and a method of preparing themixed conductor will be described in greater detail.

In the electrodes of an electrochemical device, an organic liquidelectrolyte may be used as an ionic conductor, and a carbonaceousconducting agent may be used as an electronic conductor, for example.However, and while not wanting to be bound by theory, it is understoodthat an organic liquid electrolyte and a carbonaceous conducting agentmay easily decomposed by a radical generated from an electrochemicalreaction, leading to deterioration of battery performance. Furthermore,it is understood that in an electrode, a carbonaceous conducting agentmay hinder diffusion and/or migration of ions, and an organic liquidelectrolyte may hinder migration of electrons, thus increasing internalresistance of a battery.

According to an aspect of the disclosure, there is provided a mixedconductor represented by Formula 1.

A_(1±x)M_(2±y)O_(4−δ)  Formula 1

In Formula 1, A is be a monovalent cation, M is at least one of amonovalent cation, a divalent cation, a trivalent cation, a tetravalentcation, a pentavalent cation, or a hexavalent cation, 0≤x≤1, 0≤y≤2, and0≤δ1, with the proviso that when M includes vanadium, 0<δ≤1, and whereinthe mixed conductor has an inverse spinel crystal structure.

The mixed conductor exhibits improved ionic conductivity and electronicconductivity at the same time. Also, the mixed conductor is an inorganicoxide and is understood to be chemically stable in the presence of aradical, e.g., a radical from resulting from an electrochemicalreaction, and thus may exhibit improved properties relative to othermaterials.

In an embodiment, A may be a monovalent alkali metal cation. In anaspect, the mixed conductor may be represented by Formula 2.

Li_(1±x)M_(2±y)O_(4−δ)  Formula 2

In Formula 2, L may be a monovalent alkali metal cation, and M may be atleast one of a monovalent cation, a divalent cation, a trivalent cation,a tetravalent cation, a pentavalent cation, or a hexavalent cation. δdenotes an oxygen vacancy content, 0≤y≤1, 0≤y≤2, and 0≤δ≤1, with theproviso that when M includes vanadium (V), 0<δ, e.g., 0<δ≤1. In Formula2, M is at least one metal element.

In an embodiment, L in the mixed conductor of Formula 2 may include atleast one of Li, Na, or K. Use of Li is mentioned.

In an aspect, M may be at least one metal element. For example, M in themixed conductor may include at least one of Co, Ni, Fe, Mn, V, Ti, Cr,Cu, Zn, Mo, Ru, Nb, Ta, Pd, Ag, Mg, Ca, Sr, Sc, Y, La, Ce, Pr, Nd, Sm,Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Zr, Hf, Nb, Ta, W, Tc, Re, Ru, Os,Rh, Ir, Pd, Pt, Au, Cd, Hg, Al, Ga, In, TI, Ge, Sn, Pb, Sb, Bi, Po, As,Se, or Te.

In an embodiment, the mixed conductor may be represented by Formula 3.

Li_(1±x)M_(2±y)O_(4−δ)  Formula 3

In Formula 3, M may include at least one of Co, Ni, Fe, Mn, V, Ti, Cr,Cu, Zn, Mo, Ru, Nb, Ta, Pd, Ag, Mg, Ca, Sr, Sc, Y, La, Ce, Pr, Nd, Sm,Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Zr, Hf, Nb, Ta, W, Tc, Re, Ru, Os,Rh, Ir, Pd, Pt, Au, Cd, Hg, Al, Ga, In, TI, Ge, Sn, Pb, Sb, Bi, Po, As,Se, or Te. δ may denote an oxygen vacancy content, 0≤x≤1, 0≤y≤2, and0≤δ≤1, and when M includes vanadium (V), 0<δ, e.g., 0<δ≤1.

δ may denote an oxygen vacancy content. In Formulae 1 to 3, 0≤δ≤1,0≤δ≤0.8, 0≤δ≤0.6, 0≤δ≤0.4, 0≤δ≤0.2, 0≤δ≤0.1, 0<δ≤0.8, 0.1<δ≤0.6,0.2<δ≤0.4, 0.3<δ≤0.2, or 0<δ≤0.1.

In Formulae 1 to 3, M may be located in a tetrahedral site and anoctahedral site of the inverse spinel crystal structure, e.g., M may belocated in both a tetrahedral site and in an octahedral site of theinverse spinel crystal structure. Unlike the inverse spinel crystalstructure, in a normal spinel crystal structure, M is located only in 8octahedral sites, and a monovalent cation, e.g., A, L, or lithium, islocated in a tetrahedral site.

In Formulae 1 to 3, M in the tetrahedral site may be at least one of amonovalent cation, a divalent cation, a trivalent cation, a tetravalentcation, a pentavalent cation, or a hexavalent cation, and the at leastone cation belongs to a high spin system including three or moreunpaired electrons in d-orbital. While not wanting to be bound bytheory, it is understood that due to the metal cation M belonging tosuch a high spin system, the inverse spinel crystal structure may beeasily obtained. In Formulae 1 to 3, M in the tetrahedral site may be atleast one of Fe, V, Co, Ni, Mn, Ti, Cr, Cu, Zn, Mo, Ru, Nb, Ta, Pd, orAg. In Formulae 1 to 3, M in the tetrahedral site and M in theoctahedral site may have different oxidation numbers. For example, M maycomprise Fe²⁺ and Fe³⁺, for example.

In an embodiment, the mixed conductor may be represented by Formula 4.

[M′_(1±y)]_(tet)[Li_(1±x)M″_(1±y)]_(oct)O_(4−δ)  Formula 4

In Formula 4, M′ and M″ may each independently include at least one ofCo, Ni, Fe, Mn, V, Ti, Cr, Cu, Zn, Mo, Ru, Nb, Ta, Pd, Ag, Mg, Ca, Sr,Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Zr, Hf,Nb, Ta, W, Tc, Re, Ru, Os, Rh, Ir, Pd, Pt, Au, Cd, Hg, Al, Ga, In, TI,Ge, Sn, Pb, Sb, Bi, Po, As, Se, or Te, 0≤x≤1, 0≤y≤2, and 0≤δ≤1, with theproviso that when M includes vanadium, 0<δ, e.g., 0≤δ≤1. In Formula 4,M′ may be located in a tetrahedral site ([ ]_(tet)), M″ may be locatedin an octahedral site ([ ]_(oct)), and lithium (Li) may be located in anoctahedral site ([ ]_(oct)). For example, in Formula 4, M′ may have anoxidation number of +3, +4, or +5, and M″ may have an oxidation numberof +2, +3, +4, or +5. For example, M′ and M″ may have differentoxidation numbers. In an aspect, for example, M′ and M″ are a sameelement and have different oxidation numbers, e.g., Fe²⁺ and Fe³⁺. δ maydenote an oxygen vacancy content. In an aspect, 0≤δ≤1, 0≤δ≤0.8, 0≤0≤0.6,0≤δ≤0.4, 0≤δ≤0.2, 0≤δ≤0.1, 0<δ≤0.8, 0.1<δ≤0.6, 0.2<δ≤0.4, 0.3<δ≤0.2, or0<δ≤0.1

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Fe_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ni_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Co_(2±y)O_(4−δ)(wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Mn_(2±y)O_(4−δ) (wherein 0≤δ≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)V_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0<δ≤0.5),Li_(1±x)Ti_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Cr_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Cu_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Zn_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Mo_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ru_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Nb_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ta_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Pd_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ag_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Zr_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Hf_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Nb_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ta_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)W_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Tc_(2±y)O _(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Re_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ru_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Os_(2±y)O_(4−δ) (wherein 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Rh_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ir_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Pd_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Pt_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Au_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Cd_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Hg_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Al_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ga_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)n_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Tl_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Ge_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Sn_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Pb_(2±y)O_(4−δ) (wherein 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Sb_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Bi_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5),Li_(1±x)Po_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5), orLi_(1±x)As_(2±y)O_(4−δ) (wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Fe_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Ni_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Mn_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Fe_(1±a)V_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Ti_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Cr_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Fe_(1±a)Cu_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Mo_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Fe_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Fe_(1±a)Ta_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Fe_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), or Li_(1±x)Fe_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)V_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)V_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)V_(1±a)Ni_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)V_(1±a)Mn_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)V_(1±a)Ti_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)V_(1±a)Cr_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0<δ≤0.5),Li_(1±x)V_(1±a)Cu_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0<δ≤0.5), Li_(1±x)V_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0<δ≤0.5), Li_(1±x)V_(1±a)Mo_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0<δ≤0.5),Li_(1±x)V_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0<δ≤0.5), Li_(1±x)V_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0<δ≤0.5), Li_(1±x)V_(1±a)Ta_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0<δ≤0.5),Li_(1±x)V_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0<δ≤0.5), or Li_(1±x)V_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0<δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Co_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Mn_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Co_(1±a)Ti_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Cu_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Co_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Mo_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Ru_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Co_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Ta_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Co_(1±a)Pd_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Co_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Ni_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Mn_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ni_(1±a)V_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Ti_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Cr_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ni_(1±a)Cu_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Mo_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ni_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ni_(1±a)Ta_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ni_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), or Li_(1±x)Ni_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Mn_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Mn_(1±a)Ti_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Cu_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Mn_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Mo_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Ru_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Mn_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Ta_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mn_(1±a)Pd_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Mn_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Ti_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ti_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti₁±_(a)Cu_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti_(1±a)Zn_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ti_(1±a)Mo_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti_(1±a)Nb_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ti_(1±a)Ta_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ti_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Ti_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Cr_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cr_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cr_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Cr_(1±a)Cu_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cr_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cr_(1±a)Mo_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Cr_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cr_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cr_(1±a)Ta_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Cr_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), or Li_(1±x)Cr_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Cu_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cu_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cu_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Cu_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cu_(1±a)Zn_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cu_(1±a)Mo_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Cu_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cu_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Cu_(1±a)Ta_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Cu_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), or Li_(1±x)Cr_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Zn_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Zn_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Zn_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Zn_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Zn_(1±a)Mo_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Zn_(1±a)Ru_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Zn_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Zn_(1±a)Ta_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Zn_(1±a)Pd_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Zn_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Mo_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mo_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mo_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Mo_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mo_(1±a)Ru_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mo_(1±a)Nb_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Mo_(1±a)Ta_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Mo_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Mo_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Ru_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ru_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ru_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ru₁±_(a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ru_(1±a)Nb_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ru_(1±a)Ta_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ru_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), or Li_(1±x)Ru_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Nb_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Nb_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Nb_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Nb_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Nb_(1±a)Ta_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Nb_(1±a)Pd_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Nb_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Ta_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ta_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ta_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ta_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ta_(1±a)Pd_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), orLi_(1±x)Ta_(1±a)Ag_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Pd_(1±a)Co_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Pd_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Pd_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Pd_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), or Li_(1±x)Pd_(1±a)Ag_(1±b)O_(4−δ) (wherein0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5).

In an embodiment, the mixed conductor may be at least one ofLi_(1±x)Ag_(1±a)Co_(1±b)O_(4 −δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ag_(1±a)Fe_(1±b)O_(4−δ) (wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5), Li_(1±x)Ag_(1±a)V_(1±b)O_(4−δ)(wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and 0≤δ≤0.5),Li_(1±x)Ag_(1±a)Cr_(1±b)O_(4−δ) (wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and 0≤δ≤0.5).

The mixed conductor according to an embodiment may have an electronicconductivity greater than an ionic conductivity at the same temperature.The mixed conductor according to an embodiment exhibits both suitableionic conductivity and suitable electronic conductivity at the sametime, and the ionic conductivity may be greater than the electronicconductivity. For example, the ionic conductivity of the mixed conductormay be about 1 time or greater, about 1.5 times or greater, about 2times or greater, about 2.5 times or greater, about 3 times or greater,about 3.5 times or greater, or about 4 times or greater, e.g., about 1time to about 10 times, about 1.5 times to about 10 times, about 2 timesto about 10 times, about 2.5 times to about 10 times, about 3 times toabout 10 times, about 3.5 times to about 10 times, or about 4 times toabout 10 times greater than the electronic conductivity thereof at thesame temperature. For example, the ionic conductivity of the mixedconductor may be greater than that of Li₄Ti₅O₁₂ by about 1×10 Siemensper centimeter (S/cm) or greater at the same temperature. For example, aratio of the ionic conductivity of the mixed conductor to the electronicconductivity of the mixed conductor may be about 100 to about 1, about90 to about 2, or about 50 to about 5.

In an embodiment, the mixed conductor may have an electronicconductivity of about 1.0×10⁻⁷ S/cm or greater, about 5.0×10⁻⁷ S/cm orgreater, about 1.0×10⁻⁶ S/cm or greater, about 5.0×10⁻⁶ S/cm or greater,about 1.0×10⁻⁵ S/cm or greater, or about 1.0×10⁻⁴ S/cm or greater, e.g.,about 1×10⁻⁷ S/cm to about 1×10⁻³ S/cm, about 5×10⁻⁷ S/cm about 5×10⁻⁴S/cm, about 1×10⁻⁶ S/cm to about 1×10⁻⁴ S/cm, or about 5×10⁻⁶ S/cm toabout 5×10⁻⁵ S/cm at room temperature, e.g., at 25° C. Due to the mixedconductor having such a high electronic conductivity, an electrochemicaldevice including the mixed conductor according to an embodiment may havedecreased internal resistance.

In an embodiment, the mixed conductor may have an ionic conductivity ofabout 5.0×10⁻⁷ S/cm or greater, about 1.0×10⁻⁶ S/cm or greater, about5.0×10⁻⁶ S/cm or greater, about 1.0×10⁻⁵ S/cm or greater, or about1.0×10⁻⁴ S/cm at room temperature e.g., about 1×10⁻⁶ S/cm to about1×10⁻³ S/cm, about 5×10⁻⁶ S/cm about 5×10⁻⁴ S/cm, or about 1×10⁻⁵ S/cmto about 1×10⁻⁴ S/cm, e.g., at 25 ° C. Due to the mixed conductor havingsuch a high ionic conductivity, an electrochemical device including themixed conductor according to an embodiment may have decreased internalresistance.

The electronic conductivity may be determined by an eddy current methodor a kelvin bridge method. The electrical conductivity can be determinedaccording to ASTM B-193, “Standard Test Method for Resistivity ofElectrical Conductor Materials,” e.g., at 25° C., or according to ASTME-1004, “Standard Test Method for Determining Electrical ConductivityUsing the Electromagnetic (Eddy-Current) Method,” e.g., at 25° C.Additional details may be determined by one of skill in the art withoutundue experimentation.

Ionic conductivity may be determined by a complex impedance method at25° C., further details of which can be found in J.-M. Winand et al.,“Measurement of Ionic Conductivity in Solid Electrolytes,” EurophysicsLetters, vol. 8, no. 5, p. 447-452, 1989.

In an embodiment, the mixed conductor may exhibit a diffraction peakcorresponding to the (220) plane of the inverse spinel crystal structureat a diffraction angle of 31°±2.0° 2θ in an X-ray diffraction (“XRD”)spectrum thereof, when analyzed using Cu Kα radiation. The peak at adiffraction angle of 31°±2.0° 2θ may be a peak originating from anelement located in a tetrahedral site of the spinel crystal structure.The peak does not appear when Li is in a tetrahedral site, and appearswhen a metal other than Li is located in a tetrahedral site.Accordingly, the mixed conductor according to an embodiment may have aninverse spinel crystal structure with a metal other than lithium in thetetrahedral site of the crystal structure. Unlike the mixed conductor,in an XRD spectrum of a conductor with a normal spinel crystalstructure, a diffraction peak corresponding to the (220) plane of theinverse spinel crystal structure does not appear at a diffraction angleof 31°±2.0° 2θ, and only a peak corresponding to the normal spinelcrystal structure appears.

For example, a band gap between a valence band and a conduction band ofthe mixed conductor according to an embodiment may be less than a bandgap of Li₄Ti₅O₁₂ having a normal spinel crystal structure. For example,the mixed conductor may have a band gap between a valence ban and aconduction band of, for example, about 2 electron volts (eV) or less,about 1.8 eV or less, about 1.6 eV or less, about 1.4 eV or less, orabout 1.2 eV or less, e.g., about 2 eV to about 0.01 eV, about 1.8 eV toabout 0.05 eV, about 1.6 eV to about 0.1 eV, or about 1.4 eV to about0.5 eV. When the mixed conductor has a small band gap between thevalance band and the conduction band within these ranges, migration ofelectrons from the valence band to the conduction band may befacilitated, and the mixed conductor may have improved electronicconductivity.

The mixed conductor according to an embodiment may exhibit furtherimproved ionic conductivity due to the inclusion of an oxygen vacancy.For example, the mixed conductor according to an embodiment may exhibita state density function which is shifted near the Fermi energy (Fermienergy, Ef), due to the inclusion of an oxygen vacancy, and have adecreased band gap between the valence band and the conduction band. Asa result, the mixed conductor may have further improved electronicconductivity.

In the mixed conductor according to an embodiment, A in Formula 1 may belocated in an octahedral 16 d site of the inverse spinel crystalstructure, as illustrated in FIG. 4. Referring to FIG. 4, when A islithium, an activation energy (Ea, 16 d->8 b->16 d) for a lithiumtransition from an octahedral 16 d site to another octahedral 16 d sitevia a tetrahedral 8 b site in the mixed conductor is less than anactivation energy (Ea, 8 a->16 c->8 a) for a lithium transition from atetrahedral 8 a siteto another tetrahedral 8 a site via an octahedral 16c sitein Li₄Ti₅O₁₂ having a normal spinel crystal structure. Due to themixed conductor having a smaller activation energy when a lithiumtransition occurs, relative to Li₄Ti5O₁₂,transfer, diffusion, or acombination thereof of lithium ions in the mixed conductor may befacilitated. As a result, the mixed conductor may have an increasedionic conductivity, as compared with Li₄Ti5O₁₂.

According to an aspect of the disclosure, there is provided anelectrochemical device including the mixed conductor according to anembodiment. By the inclusion of the mixed conductor which may bechemically stable and may conduct ions and electrons at the same time,deterioration of the electrochemical device may be suppressed.

In an embodiment, the electrochemical device may be, for example, atleast one of a battery, an accumulator, a supercapacitor, a fuel cell, asensor, or an electrochromic device. However, the disclosed embodimentis not limited thereto. Any suitable electrochemical device may be used.

The battery may be, for example, a primary battery or a secondarybattery. The battery may be, for example, a lithium battery, a sodiumbattery, or the like. However, the disclosed embodiment is not limitedthereto. Any suitable type of battery may be used. The lithium batterymay be, for example, a lithium-ion battery or a lithium-air battery.However, the disclosed embodiment is not limited thereto. Any suitabletype of lithium battery may be used. The electrochromic device may be anelectrochemical mirror, a window, a screen, or a facade. However, thedisclosed embodiment is not limited thereto. Any suitable electrochromicdevice may be used.

In an embodiment, the electrochemical device may include a cathode, andthe cathode may include the mixed conductor according to an embodiment.

In an embodiment, the electrochemical device including the mixedconductor according to an embodiment may be, for example, a lithium-airbattery. The lithium-air battery may include a cathode. The cathode maybe an air electrode. For example, the cathode may be arranged on acathode current collector.

The cathode may include the mixed conductor according to an embodiment.An amount of the mixed conductor in the cathode may be, for example, ina range of greater than 0 weight percent (wt %) to about 100 wt %, about0.1 wt % to about 100 wt %, about 1 wt % to about 99 wt %, about 5 wt %to about 95 wt %, or about 10 wt % to about 90wt %, each based on atotal weight of the cathode.

In an embodiment, the cathode may consist of the mixed conductoraccording to an embodiment.

In an embodiment, the cathode may further include, in addition to themixed conductor, other materials which may be used in lithium-airbatteries, for example, a conductive material, a catalyst, a binder, orthe like.

The cathode may further include a conductive material. For example, theconductive material may be porous. Due to the porosity of the conductivematerial, air permeation may be facilitated. The conductive material maybe any suitable material having porosity, conductivity, or a combinationthereof. For example, the conductive material may be a carbonaceousmaterial having porosity. The carbonaceous material may be, for example,carbon black, graphite, graphene, activated carbon, carbon fiber, or acombination thereof. However, the disclosed embodiment is are notlimited thereto. Any suitable carbonaceous material may be used. Theconductive material may be, for example, a metallic material. Forexample, the metallic material may be metal fiber, metal mesh, metalpowder, or the like. The metal powder may be, for example, copper,silver, nickel, or aluminum in powder form. The conductive material maybe, for example, an organic conductive material. The organic conductivematerial may be, for example, polyphenylene derivatives, polythiophenederivatives, or the like. For example, the above-listed conductivematerials may be used alone or in a combination thereof.

In an embodiment, the cathode may further include a catalyst foroxidation/reduction of oxygen. Examples of the catalyst may include:precious metal-based catalysts such as platinum, gold, silver,palladium, ruthenium, rhodium, and osmium; oxide-based catalysts such asmanganese oxide, iron oxide, cobalt oxide, and nickel oxide; and anorganic metal-based catalyst such as cobalt phthalocyanine. However, thedisclosed embodiment is not limited thereto. Any suitable catalyst foroxidation/reduction of oxygen may be used.

In an embodiment, the catalyst may be supported on a support. Thesupport may be an oxide support, a zeolite support, a clay-based mineralsupport, a carbon support, or the like. The oxide support may be a metaloxide support including at least one metal of aluminum (Al), silicon(Si), zirconium (Zr), titanium (Ti), cerium (Ce), praseodymium (Pr),samarium (Sm), europium (Eu), terbium (Tb), thulium (Tm), ytterbium(Yb), antimony (Sb), bismuth (Bi), vanadium (V), chromium (Cr),manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu),niobium (Nb), molybdenum (Mo), or tungsten (W). Examples of the oxidesupport may include alumina, silica, zirconium oxide, and titaniumdioxide. Examples of the carbon support may include carbon blacks suchas Ketjen black, acetylene black, channel black, and lamp black;graphite such as natural graphite, artificial black, and expandablegraphite; activated carbons; and carbon fibers. However, the disclosedembodiment is are not limited thereto. Any suitable catalyst support maybe used.

In an embodiment, the cathode may further include a binder. For example,the binder may include a thermoplastic resin or a thermocurable resin.For example, the binder may be polyethylene, polypropylene,polytetrafluoroethylene (“PTFE”), polyvinylidene fluoride (“PVdF”),styrene-butadiene rubber, a tetrafluoroethylene-perfluoroalkyl vinylether copolymer, a vinylidene fluoride-hexafluoropropylene copolymer, avinylidene fluoride-chlorotrifluoroethylene copolymer, anethylene-tetrafluoroethylene copolymer, polychlorotrifluoroethylene, avinylidene fluoride-pentafluoropropylene copolymer, apropylene-tetrafluoroethylene copolymer, anethylene-chlorotrifluoroethylene copolymer, a vinylidenefluoride-hexafluoropropylene-tetrafluoroethylene copolymer, a vinylidenefluoride-perfluoromethyl vinyl ether-tetrafluoroethylene copolymer, oran ethylene-acrylic acid copolymer, which may be used alone or in acombination thereof. However, the disclosed embodiment is are notlimited thereto. Any suitable binder may be used.

In an embodiment, the cathode may be manufactured by mixing the mixedconductor according to an embodiment, a conductive material, a catalystfor oxidation/reduction of oxygen, and a binder together and adding anappropriate solvent thereto to prepare a cathode slurry, and coating thecathode slurry on a surface of a substrate and drying a coatedresultant, or optionally compression-molding a dried product to improvean electrode density. For example, the substrate may be a cathodecurrent collector, a separator, or a solid electrolyte membrane. Forexample, the cathode current collector may be a gas diffusion layer. Theconductive material may be, for example, a composite conductor. Forexample, the conductive material, the catalyst for oxidation/reductionof oxygen and the binder may be omitted according to a type of thecathode.

In an embodiment, the lithium-air battery may include an anode. Theanode may include lithium.

In an embodiment, the anode may be, for example, a lithium metal thinfilm or a lithium-based alloy thin film. The lithium-based alloy may be,for example, a lithium alloy with, for example, aluminum, tin,magnesium, indium, calcium, titanium, or vanadium. For example, theanode may include the mixed conductor according to an embodiment.

In an embodiment, the lithium-air battery may include an electrolytemembrane between the cathode and the anode.

For example, the electrolyte membrane may include at least one of asolid electrolyte, a gel electrolyte, or a liquid electrolyte. The solidelectrolyte, the gel electrolyte, and the liquid electrolyte are notspecifically limited. Any suitable electrolyte may be used. For example,the electrolyte membrane may include the mixed conductor according to anembodiment.

In an embodiment, the solid electrolyte may include at least one of asolid electrolyte including an ionically conducting inorganic material,a solid electrolyte including a polymeric ionic liquid (“PIL”) and alithium salt, a solid electrolyte including an ionically conductingpolymer and a lithium salt, or a solid electrolyte including anelectronically conducting polymer. However, the disclosed embodiment isnot limited thereto. Any suitable solid electrolyte may be used.

For example, the ionically conducting inorganic material may include atleast one of a glass or amorphous metal ion conductor, a ceramic activemetal ion conductor, or a glass ceramic active metal ion conductor.However, the disclosed embodiment is not limited thereto. Any suitableionically conducting inorganic material may be used. For example, theionically conducting inorganic material may be ionically conductinginorganic particles or a molded product thereof, for example, in sheetform.

For example, the ionically conducting inorganic material may be at leastone of BaTiO₃, Pb(Zr_(a)Ti_(1−a))O₃ wherein 0≤a≤1 (“PZT”),Pb_(1−x)La_(x)Zr_(1−y)Ti_(y)O₃ (“PLZT”, wherein 0x≤1 and 0≤y<1),Pb(Mg₃Nb_(2/3))O₃—PbTiO₃ (“PMN-PT”), HfO₂, SrTiO₃, SnO₂, CeO₂, Na₂O,MgO, NiO, CaO, BaO, ZnO, ZrO₂, Y₂O₃, Al₂O₃, TiO₂, SiO₂, SiC, lithiumphosphate (Li₃PO₄), a lithium titanium phosphate (Li_(x)Ti_(y)(PO₄)₃,wherein 0<x<2 and 0<y<3), a lithium aluminum titanium phosphate(Li_(x)Al_(y)Ti_(z)(PO₄)₃, wherein 0<x<2, 0<y<1, and 0<z<3),Li_(1+x+y)(Al_(a)Ga_(1−a))_(x)(Ti_(b)Ge_(1−b))_(2−x)Si_(y)P_(3−y)O₁₂(wherein and 0≤b≤1), a lithium lanthanum titanate (Li_(x)La_(y)TiO₃,wherein 0<x<2, and 0<y<3), a lithium germanium thiophosphate(Li_(x)Ge_(y)P_(z)S_(w), wherein 0<x<4, 0<y<1, 0<z<1, and 0<w<5), alithium nitride (Li_(x)N_(y), wherein 0<x<4, and 0<y<2), SiS₂-basedglass, Li_(x)Si_(y)S_(z) (wherein 0<x<3,0<y<2, and 0<z<4), P₂S₅-basedglass, Li_(x)P_(y)S_(z) (wherein 0<x<3, 0<y<3, and 0<z<7), a Li₂O-basedceramic, a LiF-based ceramic, a LiOH-based ceramic, a Li₂CO₃-basedceramic, a LiAlO₂-based ceramic, a Li₂O—Al₂O₃—SiO₂—P₂O₅ 13TiO₂—GeO₂-based ceramic, a Garnet-based ceramic (Li_(3+x)La₃M₂O₁₂,wherein M=Te, Nb, or Zr)), or a combination thereof.

For example, the polymeric ionic liquid (“PIL”) may include a repeatingunit including: i) a cation of at least one of an ammonium-based cation,a pyrrolidinium-based cation, a pyridinium-based cation, apyrimidinium-based cation, an imidazolium-based cation, apiperidinum-based cation, a pyrazolium-based cation, an oxazolium-basedcation, a pyridazinium-based cation, a phosphonium-based cation, asulfonium-based cation, or a triazolium-based cation; and ii) at leastone anion of BF₄—, PF₆—, AsF₆—, SbF₆—, AlCl₄—, HSO₄—, ClO₄—, CH₃SO₃—,CF₃CO₂—, (CF₃SO₂)₂N—, Cl—,Br—, I—, SO₄—, CF₃SO₃—, (C₂F₅SO₂)₂N—,(C₂F₅SO₂)(CF₃SO₂)N—, NO₃—, Al₂Cl₇—, CF₃COO—, CH₃COO—, CF₃SO₃ —,(CF₃SO₂)₃C—, (CF₃CF₂SO₂)₂N—, (CF₃)₂PF₄—, (CF₃)₃PF₃—, (CF₃)₄PF₂—,(CF₃)₅PF—, (CF₃)—, SF₅CF₂SO₃—, SF₅CHFCF₂SO₃—, CF₃CF₂(CF₃)₂CO—,(CF₃SO₂)₂CH—, (SF₅)₃C—, (O(CF₃)₂C₂(CF₃)₂O)₂PO—, or (CF₃SO₂)₂N—. Forexample, the polymeric ionic liquid (“PIL”) may bepoly(diallyldimethylammonium) bis ((trifluoromethanesulfonyl)imide(“TFSI”)), poly(1-allyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide), andpoly((N-methyl-N-propylpiperidinium bis(trifluoromethanesulfonyl)imide.

The ionically conducting polymer may include at least one ion conductiverepeating unit of an ether-based monomer, an acryl-based monomer, amethacryl-based monomer, or a siloxane-based monomer.

The ionically conducting polymer may include, for example, polyethyleneoxide (“PEO”), polyvinyl alcohol (“PVA”), polyvinyl pyrrolidone (“PVP”),polyvinyl sulfone, polypropylene oxide (“PPO”), polymethylmethacrylate,polyethylmethacrylate, polydimethylsiloxane, polyacrylic acid,polymethacrylic acid , poly(methyl acrylate), poly(ethyl acrylate),poly(2-ethylhexyl acrylate), poly(butyl methacrylate), poly(2-ethylhexylmethacrylate), poly(decyl acrylate), polyethylene vinyl acetate, aphosphate ester polymer, polyester sulfide, polyvinylidene fluoride(“PVdF”), or Li-substituted Nafion. However, the disclosed embodiment isnot limited thereto. Any suitable ionically conducting polymer may beused.

The electronically conducting polymer may be, for example, apolyphenylene derivative or a polythiophene derivative. However, thedisclosed embodiment is not limited thereto. Any suitable electronicallyconducting polymer may be used.

In an embodiment, the gel electrolyte may be obtained, for example, byadding a low-molecular weight solvent to a solid electrolyte interposedbetween the cathode and the anode. The gel electrolyte may be a gelelectrolyte obtained by further adding a low-molecular weight organiccompound such as a solvent, an oligomer, or the like to the polymer. Thegel electrolyte may be a gel electrolyte obtained by further adding alow-molecular weight organic compound such as a solvent or an oligomerto any of the above-listed polymer electrolytes.

In an embodiment, the liquid electrolyte may include a solvent and alithium salt. The solvent may include at least one of an organicsolvent, an ionic liquid (“IL”), or an oligomer. However, the disclosedembodiment is are not limited thereto. Any suitable solvent that is inliquid form at room temperature (25° C.) may be used.

The organic solvent may include, for example, at least one of anether-based solvent, a carbonate-based solvent, an ester-based solvent,or a ketone-based solvent. For example, the organic solvent may includeat least one of propylene carbonate, ethylene carbonate, fluoroethylenecarbonate, vinylethylene carbonate, butylene carbonate, dimethylcarbonate, diethyl carbonate, methylethyl carbonate, methylpropylcarbonate, ethylpropyl carbonate, methylisopropyl carbonate, dipropylcarbonate, dibutyl carbonate, benzonitrile, acetonitrile,tetrahydrofuran, 2-methyltetrahydrofuran, y-butyrolactone, dioxorane,4-methyldioxorane, dimethyl acetamide, dimethylsulfoxide, dioxane,1,2-dimethoxyethane, sulfolane, dichloroethane, chlorobenzene,nitrobenzene, succinonitrile, diethylene glycol dimethyl ether(“DEGDME”), tetraethylene glycol dimethyl ether (“TEGDME”), polyethyleneglycol dimethyl ether (“PEGDME”, number average molecular weight(Mn)=˜500), dimethyl ether, diethyl ether, dibutyl ether,dimethoxyethane, 2-methyltetrahydrofuran, or tetrahydrofuran. However,the disclosed embodiment is not limited thereto. The organic solvent maybe any suitable organic solvent that is in liquid form at roomtemperature.

The ionic liquid (“IL”) may include, for example, i) at least one cationof an ammonium-based cation, a pyrrolidinium-based cation, apyridinium-based cation, a pyrimidinium-based cation, animidazolium-based cation, a piperidinium-based cation, apyrazolium-based cation, an oxazolium-based cation, a pyridazinium-basedcation, a phosphonium-based cation, a sulfonium-based cation, or atriazolium-based cation, and ii) at least one anion of BF₄—, PF₆—,AsF₆—, SbF₆—, AlCl₄—, HSO₄—, ClO₄—, CH₃SO₃—, CF₃CO₂—, (CF₃SO₂)₂N—, Cl—,Br—, I—, BF₄—, SO₄—, PF₆—, ClO₄—, CF₃SO₃—, CF₃CO₂—, (C₂F₅SO₂)₂N—,(C₂F₅SO₂)(CF₃SO₂)N—, NO₃—, Al₂Cl₇—, ASF₆—, SbF₆—, CF₃COO—, CH₃COO—,CF₃SO₃—, (CF₃SO₂)₃C—, (CF₃CF₂SO₂)₂N—, (CF₃)₂PF₄—, (CF₃)₃PF₃—,(CF₃)₄PF₂—, (CF₃)₅PF—, (CF₃)₆P—, SF₅CF₂SO₃—, SF₅CHFCF₂SO₃—,CF₃CF₂(CF₃)₂CO—, (CF₃SO₂)₂CH—, (SF₅)₃C—, (O(CF₃)₂C₂(CF₃)₂O)₂PO—, or(CF₃SO₂)₂N—.

The lithium salt may include at least one of Lithiumbis(trifluoromethanesulfonyl)imide (“LiTFSI”), LiPF₆, LiBF₄, LiAsF₆,LiClO₄, LiNO₃, (lithium bis(oxalato) borate(LiBOB), LiCF₃SO₃,LiN(SO₂CF₃)₂, LiN(SO₂C₂F₅)₂, LiC(SO₂CF₃)₃, LiN(SO₃CF₃)₂, LiC₄F₉SO₃,LiAlCl₄, or lithium trifluoromethanesulfonate (“LiTf0”) However, thedisclosed embodiment is not limited thereto. Any suitable lithium saltmaterial may be used. A concentration of the lithium salt may be, forexample, about 0.01 M to about 5.0 M.

In an embodiment, the lithium-air battery may further include aseparator between the cathode and the anode. Any suitable separator maybe used as long as being durable under operation conditions of thelithium-air battery. For example, the separator may include a polymernon-woven fabric, for example, a non-woven fabric of polypropylenematerial or a non-woven fabric of polyphenylene sulfide; a porous filmof an olefin resin such as polyethylene or polypropylene; or glassfiber. Two or more separators may be used.

For example, the electrolyte membrane may have a structure in which asolid polymer electrolyte is impregnated in the separator, or astructure in which a liquid electrolyte is impregnated in the separator.For example, the electrolyte membrane in which a solid polymerelectrolyte is impregnated in the separator may be prepared by arrangingsolid polymer electrolyte films on opposite surfaces of the separator,and roll-pressing them at the same time. For example, the electrolytemembrane in which a liquid electrolyte is impregnated in the separatormay be prepared by injecting a liquid electrolyte including a lithiumsalt into the separator.

In an embodiment, the lithium-air battery may be manufactured byinstalling the anode on an inner side of a case, sequentially arrangingthe electrolyte membrane on the anode, the cathode on the electrolytemembrane, and a porous cathode current collector on the cathode, andthen arranging a pressing member on the porous cathode current collectorto press a resulting cell structure with the pressing member so as toallow air to be transferred to the air electrode (i.e., cathode). Thecase may be divided into upper and lower portions which contact theanode and the air electrode, respectively. An insulating resin may bedisposed between the upper and lower portions of the case toelectrically insulate the cathode and the anode from one another.

The lithium-air battery according to an embodiment may be used as alithium primary battery or a lithium secondary battery. The lithium-airbattery may have any suitable shape of, for example, a coin, a button, asheet, a stack, a cylinder, a plane, or a horn. However, the disclosedembodiment is not limited thereto. The lithium-air battery may be usedin a large battery for electric vehicles.

FIG. 5 is a schematic view illustrating a structure of a lithium-airbattery 500 according to an embodiment. Referring to FIG. 5, thelithium-air battery 500 according to an embodiment may include a cathode200 adjacent to a first current collector 210 and using oxygen as anactive material, an anode 300 adjacent to a second current collector 310and including lithium, and an first electrolyte membrane 400 interposedbetween the cathode 200 and the anode 300. The first electrolytemembrane 400 may be a separator impregnated with a liquid electrolyte. Asecond electrolyte membrane 450 may be arranged between the cathode 200and the first electrolyte membrane 400. The second electrolyte membrane450 may be a lithium-ion conductive solid electrolyte membrane. Thefirst current collector 210 may be porous and function as a gasdiffusion layer which allows diffusion of air. A pressing member 220 fortransporting air to the cathode 200 may be arranged on the first currentcollector 210. A case 320 made of an insulating resin may be disposedbetween the cathode 200 and the anode 300 to electrically insulate thecathode 200 and the anode 300 from one another. The air may be suppliedinto the lithium-air battery 500 through an air inlet 230 a and may bedischarged through an air outlet 230 b. The lithium-air battery 500 maybe accommodated in a stainless steel container.

The term “air” used herein is not limited to atmospheric air, and forconvenience, may refer to a combination of gases including oxygen, orpure oxygen gas. This broad definition of the term “air” also applies toother terms used herein, including “air battery” and “air electrode.”

According to an aspect of the disclosure, a method of preparing themixed conductor according to an embodiment includes: mixing an A-elementprecursor, e.g., an A-element containing precursor, and an M-elementprecursor, e.g., an M-element containing precursor, to prepare amixture; and reacting the mixture in a solid phase to thereby preparethe mixed conductor. Due to the preparation of the mixed conductorthrough the solid state reaction, it may be possible to produce themixed conductor on a mass scale.

In the preparation of the mixture, for example, the A-element precursorand the M-element precursor may be mixed in an organic solvent, anaqueous solution, or a combination thereof with a ball mill. The organicsolvent may be alcohol such as 2-propanol. However, the disclosedembodiment is not limited thereto. Any suitable solvent may be used. Thereacting of the mixture in a solid phase may mean that the reactionproceeds, for example, by heat treatment in the absence of a solvent.

For example, the prepared mixed conductor may be represented by Formula1.

A_(1±x)M_(2±y)O_(4−δ)  Formula 1

In Formula 1, A may be a monovalent cation, and M may be at least one ofa monovalent cation, a divalent cation, a trivalent cation, atetravalent cation, a pentavalent cation, or a hexavalent cation, δdenotes oxygen vacancy, 0≤x≤1, 0≤y≤2, and 0≤δ≤1, and when M is vanadium(V), 0<δ.

In the method according to an embodiment, the A-element precursor maybe, for example, a salt or an oxide of A, and the M-element precursormay be, for example, a salt or an oxide of M.

For example, the A-element precursor may be a lithium precursor. Thelithium precursor may be, for example, Li₂CO₃, LiNO₃, LiNO₂, LiOH,LiOH·nH₂O, LiH, LiF, LiCl, LiBr, Lil, CH₃OOLi, Li₂O, Li₂SO₄, lithiumdicarboxylate, lithium citrate, lithium fatty acid, or alkyl lithium.However, the disclosed embodiment is not limited thereto. Any suitablelithium precursor may be used.

The M-element precursor may be, for example, a precursor of at least onemetal of Co, Ni, Fe, Mn, V, Ti, Cr, Cu, Zn, Mo, Ru, Nb, Ta, Pd, Ag, Mg,Ca, Sr, Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu,Zr, Hf, Nb, Ta, W, Tc, Re, Ru, Os, Rh, Ir, Pd, Pt, Au, Cd, Hg, Al, Ga,In, TI, Ge, Sn, Pb, Sb, Bi, Po, As, Se, or Te. For example, theM-element precursor may be at least one of a Co precursor, a Niprecursor, a Fe precursor, a Mn precursor, or a V precursor. The Coprecursor may be, for example, CoO, Co₂O₃, Co₃O₄, CoF₂, Co(OCH₃)₂,CoCl₂, or the like. However, the disclosed embodiment is not limitedthereto. Any suitable Co precursor may be used. The Ni precursor may be,for example, NiO, Ni₂O₃, NiF₂, NiCl₂, NiBr₂, or Ni(OCH₃)₂. However, thedisclosed embodiment is not limited thereto. Any suitable Ni precursormay be used. The Fe precursor may be, for example, FeCl₃, FeF₃,Fe(NO₃)₃, FeSO₄, FeO, or Fe₂O₃. However, the disclosed embodiment is notlimited thereto. Any suitable Fe precursor may be used. The Mn precursormay be, for example, Mn(NO₃)₂, MnSO₄, MnO, Mn₂O₃, MnCl₂, or MnF₂.However, the disclosed embodiment is not limited thereto. Any suitableMn precursor may be used. The V precursor may be, for example, VO(NO₃)₃,VOSO₄, V₂O₅, VCl₂, VCl₃, or VF₃. However, the disclosed embodiment isnot limited thereto. Any suitable V precursor may be used.

In the mixed conductor preparation method according to an embodiment,the preparing of the mixed conductor by reacting the mixture in a solidphase may include: performing first thermal treatment on the mixtureunder a dry and oxidizing condition to prepare a first thermal treatmentproduct; grinding and pressing the first thermal treatment product tothereby prepare pellets; and performing second thermal treatment on thepellets under a) a reducing condition, b) an oxidizing condition, or c)an oxidizing and reducing condition.

In the second thermal treatment, a) the reducing condition, b) theoxidizing condition, or c) the oxidizing and reducing condition may beappropriately selected according to the oxidation number of a metal inthe mixed conductor to be prepared.

The a) reducing condition may be a condition including a reducing gas.The reducing gas may be, for example, hydrogen (H₂). However, thedisclosed embodiment is not limited thereto. Any suitable reducing gasmay be used. The reducing condition may include a mixture of a reducinggas and an inert gas. The inert gas may be, for example, nitrogen,argon, or the like. However, the disclosed embodiment is not limitedthereto. Any suitable inert gas may be used. In the reducing condition,an amount of the reducing gas may be, for example, about 1% to about99%, about 2% to about 50%, or about 5% to about 20%, each based on atotal volume of the entire gas. Due to the thermal treatment under sucha reducing condition, oxygen vacancies may be introduced into the mixedconductor.

The b) oxidizing condition may be a condition including an oxidizinggas. The oxidizing gas may be, for example, oxygen or air. However, thedisclosed embodiment is not limited thereto. Any suitable oxidizing gasmay be used. The oxidizing condition may include a mixture of anoxidizing gas and an inert gas. The inert gas may be the same as thatused in the above-described reducing atmosphere.

The second thermal treatment under c) an oxidizing and reducingcondition may refer to a second thermal treatment in which thermaltreatment is sequentially performed under an oxidizing condition andthen under a reducing condition. The oxidizing and reducing conditionmay be the same as a combination of a) the oxidizing condition and b)the reducing condition each described above.

The first thermal treatment may be performed, for example, at atemperature of about 400 ° C. to about 1,000 ° C., about 450 ° C. toabout 900 ° C., about 500 ° C. to about 800 ° C., or about 500 ° C. toabout 750 ° C. The first thermal treatment time may be, for example,about 2 hours to about 10 hours, about 3 hours to about 9 hours, about 4hours to about 8 hours, or about 4 hours to about 6 hours. The secondthermal treatment may be performed, for example, at a temperature ofabout 400 ° C. to about 1200 ° C., about 500 ° C. to about 1100 ° C.,about 600 ° C. to about 1,000 ° C., or about 600 ° C. to about 900 ° C.The second thermal treatment time may be, for example, about 4 hours toabout 48 hours, for example, about 6 hours to about 40 hours, about 8hours to about 30 hours, or about 10 hours to about 20 hours. Due to thefirst thermal treatment and the second thermal treatment performed undersuch conditions as described above, the prepared mixed conductor mayhave further improved electrochemical stability.

An embodiment of the present disclosure will now be described in furtherdetail with reference to the following examples. However, these examplesare only for illustrative purposes and are not intended to limit thescope of the disclosed embodiment.

EXAMPLES Preparation of Mixed Conductor Example 1: LiFe₂O₄

Li₂CO₃ as a lithium precursor and Fe₂O₃ as an iron precursor were mixedin a stoichiometric ratio, and then mixed with ethanol, followed bygrinding and mixing a resulting mixture with a ball mill includingzirconia balls at about 280 rpm for about 4 hours to thereby obtain amixture. The obtained mixture was dried at about 90 ° C. for about 6hours, and then thermally treated under an air atmosphere at about 750 °C. for about 5 hours (first thermal treatment). A first thermaltreatment product was ground using a ball mill and then pressed underisostatic pressure to thereby prepare pellets. The prepared pellets weresubjected to second thermal treatment at about 900 ° C. under an airatmosphere for about 12 hours to thereby prepare a mixed conductor(LiFe₂O₄).

Example 2: LiFeCoO₄

Li₂CO₃ as a lithium precursor, Fe₂O₃ as an iron precursor, and Co₃O₄ asa cobalt precursor were mixed in a stoichiometric ratio, and then mixedwith ethanol, followed by grinding and mixing a resulting mixture with aball mill including zirconia balls at about 280 rpm for about 4 hours tothereby obtain a mixture. The obtained mixture was dried at about 90 °C. for about 6 hours, and then thermally treated under an air atmosphereat about 750 ° C. for about 5 hours (first thermal treatment). A firstthermal treatment product was ground using a ball mill and then pressedunder isostatic pressure to thereby prepare pellets. The preparedpellets were subjected to second thermal treatment at about 900 ° C.under an air atmosphere for about 12 hours to thereby prepare a mixedconductor (LiFeCoO₄).

Example 3: LiVNiO_(4−δ)

Li₂CO₃ as a lithium precursor, V₂O₃ as a vanadium precursor, and Ni(OH)₂as a nickel precursor were mixed in a stoichiometric ratio, and thenmixed with ethanol, followed by grinding and mixing a resulting mixturewith a ball mill including zirconia balls at about 280 rpm for about 4hours to thereby obtain a mixture. The obtained mixture was dried atabout 90 ° C. for about 6 hours, and then thermally treated under an airatmosphere at about 500 ° C. for about 5 hours (first thermaltreatment). A first thermal treatment product was ground using a ballmill and then pressed under isostatic pressure to thereby preparepellets. The prepared pellets were subjected to second thermal treatmentat about 600 ° C. under an air atmosphere for about 12 hours to therebyprepare a mixed conductor (LiVNiO_(4−δ), wherein 0<δ).

Comparative Example 1: Li₄Ti₅O₁₂

Commercially purchased Li₄Ti₅O₁₂ powder was pressed under an isostaticpressure, as described in Example 1, to thereby prepare pellets.

Evaluation Example 1: X-ray Diffraction (“XRD”) Evaluation

X-ray diffraction (“XRD”) spectra of the mixed conductor of Examples 1to 3 were evaluated. The results are shown in FIG. 1. The XRD spectrawere obtained with Cu Kα radiation.

Referring to FIG. 1, the mixed conductors of Examples 1 to 3 eachexhibited peak corresponding to the (220) plane of the inverse spinelcrystal structure at a diffraction angle 2θ of 31°±2.0° 2θ.

The peak at a diffraction angle 2θ of 31°±2.0° 2θ is a peak originatingfrom an element located in a tetrahedral site of a normal spinel crystalstructure. This peak does not appear when Li is in the tetrahedral site,but appears when a metal except for Li is located in the tetrahedralsite. Accordingly, as shown in FIG. 1, the mixed conductors of Examples1 to 3 each had an inverse spinel crystal structure with a non-lithiummetal in the tetrahedral site of the spinel crystal structure.

On the contrary, in an XRD spectrum of the Li₄Ti₅O₁₂ conductor ofComparative Example 1, a diffraction peak corresponding to the (220)plane of the inverse spinel crystal structure did not appear at adiffraction angle 2θ of 31°±2.0° 2θ, but only a peak corresponding tothe normal spinel crystal structure appeared. Accordingly, the Li₄Ti₅O₁₂conductor of Comparative Example 1 had a normal spinel crystal structurewith only lithium in the tetrahedral site of the spinel crystalstructure.

Through further structure analysis, the mixed conductors of Examples 1to 3 each having the inverse spinel crystal structure had oxidationnumbers and compositions represented by [Fe³⁺]_(tet)[Li⁺Fe⁴⁺]_(oct)O₄,[Fe³⁺]_(tet)[Li⁺Co⁴⁺]_(oct)O₄, and [V⁵⁺]_(tet)[Li⁺Ni²⁺]_(oct)O_(4−δ),respectively, wherein [ ]_(tet) denotes the tetrahedral site in thespinel crystal structure, and [ ]_(oct) denotes the octahedral site inthe spinel crystal structure.

Evaluation Example 2: Evaluation of Electronic Conductivity

Ion-blocking cells were manufactured by sputtering gold (Au) ontoopposite surfaces of each of the mixed conductors in pellets prepared inExamples 1 to 3 and Comparative Preparation Example 1, and thenelectronic conductivities of the ion-blocking cells were measured usinga direct current (“DC”) polarization method at room temperature (25 °C.).

While applying a constant voltage of about 100 mV to each of thecompleted symmetric cells for about 30 minutes, a time-dependent currentof the cell was measured. An electronic resistance of each of the mixedconductors was calculated from the measured current, and an electronicconductivity was calculated from the calculated electronic resistance.The obtained electronic conductivities are shown in Table 1.

Evaluation Example 3: Evaluation of Ionic Conductivity

Electron-blocking cells were manufactured by arranging liquidelectrolyte (1 molar (M) lithium bis(trifluoromethanesulfonyl)imide(LiTFSI) in propylene carbonate (“PC”))-impregnated separator membraneson opposite surfaces of each of the mixed conductors in pellets preparedin Examples 1 to 3 and Comparative Example 1, and then arranging lithiumfoils thereon. Next, ionic conductivities of the electron-blocking cellswere measured using a DC polarization method at room temperature (25 °C.).

While applying a constant voltage of about 100 millivolts (mV) to eachof the completed symmetric cells for about 30 minutes, a time-dependentcurrent of the cell was measured. An ionic resistance of each of themixed conductors was calculated from the measured current, and an ionicconductivity was calculated from the calculated ionic resistance. Theobtained ionic conductivities are shown in Table 1.

TABLE 1 Electronic conductivity (Siemens Ionic percentimeterconductivity Example Composition (S/cm)) (S/cm) Comparative Li₄Ti₅O₁₂ 4.3 × 10⁻⁹  6.8 × 10⁻⁸ Example 1 Example 1 LiFe₂O₄ 1.32 × 10⁻⁶ 6.49 ×10⁻⁶ Example 2 LiFeCoO₄ 2.14 × 10⁻⁶ 4.72 × 10⁻⁶ Example 3 LiVNiO_(4-δ)1.56 × 10⁻⁷ 7.50 × 10⁻⁷

Referring to Table 1, the mixed conductors of Examples 1 to 3 with aninverse spinel crystal structure each had improved electronicconductivity and ionic conductivity at the same time, as compared withthe Li₄Ti₅O₁₂ conductor of Comparative Example 1 with the normal spinelcrystal structure.

The mixed conductors of Examples 1 to 3 each had an ionic conductivitygreater than an electronic conductivity.

Evaluation Example 4: Evaluation of Electronic Band Structure

The electronic band structures of the Li₄Ti₅O₁₂ conductor of ComparativeExample 1 and the mixed conductor (LiFe₂O₄) of Example 1 werecalculated, and band gaps were evaluated from the calculation results.

The electronic band structures were calculated using the Viennaab-initio simulation program (“VASP”) with the framework of densityfunctional theory (“DFT”). The calculation results of the Li₄Ti₅O₁₂conductor of Comparative Example 1 are shown in FIG. 2

Referring to FIG. 2, the conductor of Comparative Example 1 had a bandgap of about 2.5 electron volts (eV). The mixed conductors of Examples 1to 3 each had a band gap of about 2.0 volts (V) or less.

That is, the mixed conductors of Examples 1 to 3 with an inverse spinelcrystal structure each had a smaller band gap, as compared with theLi₄Ti₅O₁₂ conductor of Comparative Example 1 with the normal spinelcrystal structure, and thus have improved electronic conductivity.

Evaluation Example 5: Evaluation of Lithium Transition Activation Energy

As shown in FIG. 3, in the Li₄Ti₅O₁₂ conductor of Comparative Example 1with the normal spinel crystal structure, lithium occupied tetrahedral 8a site s and octahedral 16 d sites of a spinel-like crystal structure.Further, a face sharing octahedral 16 c siteis disposed between twoadjacent tetrahedral 8 a sites. Lithium conduction characteristics areattributed to, for example, transition of lithium from a tetrahedral 8 asiteto another tetrahedral 8 a sitevia an octahedral 16 c site .

As illustrated in FIG. 4, in the mixed conductor LiFe₂O₄ of Example 1with an inverse spinel crystal structure, lithium occupied octahedral 16d sites of the inverse spinel crystal structure, with a face sharingtetrahedral 8 b site between two adjacent octahedral 16 d sites. Lithiumconduction characteristics are attributed to, for example, a lithiumtransition from an octahedral 16 d site to another octahedral 16 d sitevia a tetrahedral 8 b site. In FIG. 4, M denotes a transition metal,i.e., iron (Fe).

A lithium transition activation energy of the Li₄Ti₅O₁₂ conductor ofComparative Example 1 when lithium transitions from a tetrahedral 8 asiteto another tetrahedral 8 a site via an octahedral 16 c sitewascalculated.

A lithium transition activation energy of the mixed conductor (LiFe₂O₄)of Example 1 when lithium transitions from an octahedral 16 d site toanother octahedral 16 d site via a tetrahedral 8 b site was calculated.

The lithium transition activation energies were calculated using theVienna abinitio simulation program (“VASP”) with the framework ofdensity functional theory (“DFT”).

The activation energy (Ea, 8 a->16 c->8 a, i.e., energy barrier) of theLi₄Ti₅O₁₂ conductor of Comparative Example 1 with the normal spinelcrystal structure when lithium transition or lithium diffusion occursfrom a tetrahedral 8 a siteto another tetrahedral 8 a sitevia anoctahedral 16 c sitewas about 0.7 eV or greater.

The activation energy (Ea, 16 d->8 b->16 d, i.e., energy barrier) of themixed conductor (LiFe₂O₄) of Example 1 with an inverse spinel crystalstructure when a lithium transition or a lithium diffusion occurs froman octahedral 16 d site from another octahedral 16 d site via atetrahedral 8 b site was about 0.6 eV or less.

Referring to Table 1 above, the mixed conductors of Examples 1 to 3 withan inverse spinel crystal structure each exhibited improved ionicconductivity, as compared with the Li₄Ti5O₁₂ conductor of ComparativeExample 1.

Accordingly, a mixed conductor having an inverse spinel crystalstructure according to an embodiment has a decreased energy barrier whenlithium transition or lithium diffusion occurs, and improved ionicconductivity.

As described above, according to an embodiment, by using a mixedconductor which may be chemically stable and conduct both ions andelectrons, deterioration of an electrochemical device may be suppressed.

It should be understood that the embodiment described herein should beconsidered in a descriptive sense only and not for purposes oflimitation. Descriptions of features or aspects within this embodimentshould be considered as available for other similar features or aspects.

While an embodiment has been described with reference to the figures, itwill be understood by those of ordinary skill in the art that variouschanges in form and details may be made therein without departing fromthe spirit and scope as defined by the following claims.

What is claimed is:
 1. A mixed conductor represented by Formula 1:A_(1±x)M_(2±y)O_(4−δ)  Formula 1 wherein, in Formula 1, A is amonovalent cation, M is at least one of a monovalent cation, a divalentcation, a trivalent cation, a tetravalent cation, a pentavalent cation,or a hexavalent cation, 0≤x≤1, 0≤y≤2, and 0≤δ≤1, with the proviso thatwhen M includes vanadium, 0<δ≤1, and wherein the mixed conductor has aninverse spinel crystal structure.
 2. The mixed conductor of claim 1,wherein A in Formula 1 is a monovalent alkali metal cation.
 3. The mixedconductor of claim 2, wherein A is at least one of Li, Na, or K.
 4. Themixed conductor of claim 1, wherein M is at least one of Co, Ni, Fe, Mn,V, Ti, Cr, Cu, Zn, Mo, Ru, Nb, Ta, Pd, Ag, Mg, Ca, Sr, Sc, Y, La, Ce,Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Zr, Hf, Nb, Ta, W, Tc,Re, Ru, Os, Rh, Ir, Pd, Pt, Au, Cd, Hg, Al, Ga, In, TI, Ge, Sn, Pb, Sb,Bi, Po, As, Se, or Te.
 5. The mixed conductor of claim 1, wherein inFormula 1 A is Li, and M is at least one of Co, Ni, Fe, Mn, V, Ti, Cr,Cu, Zn, Mo, Ru, Nb, Ta, Pd, Ag, Mg, Ca, Sr, Sc, Y, La, Ce, Pr, Nd, Sm,Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Zr, Hf, Nb, Ta, W, Tc, Re, Ru, Os,Rh, Ir, Pd, Pt, Au, Cd, Hg, Al, Ga, In, TI, Ge, Sn, Pb, Sb, Bi, Po, As,Se, or Te.
 6. The mixed conductor of claim 1, wherein M is located inboth a tetrahedral site and in an octahedral site of the inverse spinelcrystal structure.
 7. The mixed conductor of claim 6, wherein the M inthe tetrahedral site belongs to a high spin system including three ormore unpaired electrons in a d-orbital.
 8. The mixed conductor of claim6, wherein the M in the tetrahedral site is at least one of Fe, V, Co,Ni, Mn, Ti, Cr, Cu, Zn, Mo, Ru, Nb, Ta, Pd, or Ag.
 9. The mixedconductor of claim 6, wherein the M in the tetrahedral site and the M inthe octahedral site have different oxidation numbers.
 10. The mixedconductor of claim 6, wherein the mixed conductor is at least one of:Li_(1±x)Fe_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ni_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Co_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Mn_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,L_(1±x)V_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ti_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,L_(1±x)Cr_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Cu_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Zn_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Mo_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ru_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Nb_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ta_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Pd_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ag_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Zr_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Hf_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Nb_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ta_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)W_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Tc_(2±y)O_(4−δ) wherein 0≤x≤0.5 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Re_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ru_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Os_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Rh_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ir_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,L_(1±x)Pd_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Pt_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Au_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Cd_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Hg_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Al_(2±4)O_(4−δ) wherein 0≤x≤x0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ga_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)In_(2+y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Tl_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Ge_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Sn_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Pb_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Sb_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Bi_(2±y)O_(4−δ) wherein0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Po_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)As_(2±y)O_(4−δ) wherein 0≤x≤0.5, 0≤y≤1, and 0≤δ≤0.5,Li_(1±x)Fe_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Ni_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Mn_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Fe_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Ti_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Cr_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Fe_(1±a)Cu_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Mo_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Fe_(1±a)Ru_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Ta_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Fe_(1±a)Pd_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Fe_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)V_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Ni_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Mn_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)V_(1±a)Ti_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Cu_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)V_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Mo_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(a±x)V_(1±a)Ru_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)V_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)V_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)V_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Mn_(1±b)O_(4−δ)0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Co_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Ti_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Cr_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)C_(1±a)CU_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Mo_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Co_(1±a)Ru_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Ta_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Co_(1±a)Pd_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Co_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Co_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ni_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Mn_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)V_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ni_(1±a)Ti_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Cu_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ni_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Mo_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Ru_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ni_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ni_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ni_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mn_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Ti_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Cr_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mn_(1±a)Cu_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Mo_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mn_(1±a)Ru_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Ta_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mn_(1±a)Pd_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mn_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Co_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ti_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Cr_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ti_(1±a)Cu_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Mo_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ti_(1±a)Ru_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Ta_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ti_(1±a)Pd_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ti_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)Co_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cr_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)CU_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cr_(1±a)Zn_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)Mo_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)Ru_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cr_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cr_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cu_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Zn_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cu_(1±a)Mo_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Ru_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Nb_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Cu_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cu_(1±a)Pd_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Cr_(1±a)Ag_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Zn_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Zn_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Zn_(1±a)V_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Zn_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Zn_(1±a)Mo_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Zn_(1±a)Ru_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Zn_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Zn_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Zn_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Zn_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mo_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mo_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mo_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mo_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mo_(1±a)Ru_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mo_(1±a)Nb_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mo_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Mo_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Mo_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ru_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ru_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)RU_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ru_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ru_(1±a)Nb_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ru_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ru_(1±a)Pd_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ru_(1±a)Ag_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Nb_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Nb_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Nb_(1±a)V_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Nb_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Nb_(1±a)Ta_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Nb_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Nb_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ta_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ta_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ta_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ta_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ta_(1±a)Pd_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ta_(1±a)Ag_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Pd_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Pd_(1±a)Fe_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Pd_(1±a)V_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Pd_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Pd_(1±a)Ag_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5,Li_(1±x)Ag_(1±a)Co_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ag_(1±a)Fe_(1±b)O_(4−δ) wherein 0≤x≤0.5,0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, Li_(1±x)Ag_(1±a)V_(1±b)O_(4−δ)wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5, 0≤a+b≤1, and≤δ≤0.5, orLi_(1±x)Ag_(1±a)Cr_(1±b)O_(4−δ) wherein 0≤x≤0.5, 0≤a≤0.5, 0≤b≤0.5,0≤a+b≤1, and≤δ≤0.5.
 11. The mixed conductor of claim 1, wherein an ionicconductivity of the mixed conductor is greater than an electronicconductivity of the mixed conductor.
 12. The mixed conductor of claim 1,wherein the mixed conductor has an electronic conductivity of about1×10⁻⁷ Siemens per centimeter to about 1×10⁻³ Siemens per centimeter at25° C.
 13. The mixed conductor of claim 1, wherein the mixed conductorhas an ionic conductivity of about 5×10⁻⁷ Siemens per centimeter toabout 1×10⁻³ Siemens per centimeter at 25° C.
 14. The mixed conductor ofclaim 6, wherein, when analyzed by X-ray diffraction using Cu Kαradiation, the mixed conductor has a diffraction peak corresponding the(220) plane of the inverse spinel crystal structure at about 31°±2.0°2θ.
 15. The mixed conductor of claim 1, wherein a band gap between avalence band and a conduction band of the mixed conductor is less than aband gap of Li₄Ti₅O₁₂ having a spinel crystal structure.
 16. The mixedconductor of claim 15, wherein the band gap between the valence band andthe conduction band of the mixed conductor is about 2 electron volts toabout 0.1 electron volts.
 17. The mixed conductor of claim 1, whereinwhen A is located in an octahedral 16 d site of the inverse spinelcrystal structure, and when A is lithium, a lithium transitionactivation energy for a lithium transition from the octahedral 16 d siteto another octahedral 16 d site via a tetrahedral 8 b site in the mixedconductor is less than an activation energy for a lithium transitionfrom an tetrahedral 8 a siteto another tetrahedral 8 a sitevia anoctahedral 16 c site in Li₄Ti₅O₁₂ having a spinel crystal structure. 18.An electrode comprising: a current collector; and the mixed conductor ofclaim 1 on the current collector.
 19. The electrode of claim 18, furthercomprising an oxygen oxidation/reduction catalyst.
 20. Anelectrochemical device comprising: a cathode; an anode; and anelectrolyte between the cathode and the anode, wherein at least one ofthe cathode, the anode, and the electrolyte comprises the mixedconductor according to claim
 1. 21. The electrochemical device of claim20, wherein the electrochemical device is a battery, an accumulator, asupercapacitor, a fuel cell, a sensor, or an electrochromic device. 22.The electrochemical device of claim 20, wherein in the electrochemicaldevice, the cathode comprises the mixed conductor.
 23. A method ofpreparing a mixed conductor, the method comprising: mixing an A-elementcontaining precursor and an M-element containing precursor to prepare amixture; and thermally treating the mixture in a solid phase to preparethe mixed conductor.
 24. The method of claim 23, wherein the mixedconductor is represented by Formula 1:A_(1±x)M_(2±y)O_(4−δ)  Formula 1 wherein, in Formula 1, A is amonovalent cation, M is at least one of a monovalent cation, a divalentcation, a trivalent cation, a tetravalent cation, a pentavalent cation,or a hexavalent cation, 0≤x≤1, 0≤y≤2, and 0≤δ≤1, with the proviso thatwhen M includes vanadium, 0<δ≤1, and wherein the mixed conductor has aninverse spinel crystal structure.
 25. The method of claim 23, whereinthe thermally-treating comprises: first thermally treating the mixtureunder a dry and oxidizing condition to prepare a first thermal treatmentproduct; grinding the first thermal treatment product; pressing theground first thermal treatment product to thereby prepare a pellet; andsecond thermally treatment the pellets under a reducing condition, anoxidizing condition, or an oxidizing condition and reducing condition toprepare the mixed conductor.
 26. The method of claim 23, wherein theA-element containing precursor is a salt or an oxide of A, and theM-element containing precursor is a salt or an oxide of M.
 27. Themethod of claim 25, wherein the first thermally treating comprisestreating at a temperature of about 600 ° C. to about 1,000 ° C. forabout 2 hours to about 10 hours, and the second thermally treatingcomprises treating at a temperature of about 700 ° C. to about 1,400 °C. for about 6 hours to about 48 hours.